Render a cut through a mesh
One way of doing this without modifying the actual mesh at all is to use a texture to define the transparency of the mesh:

Cycles:



To create something similar to the AltB option, you could:


UV unwrap using U> project from view:


Use the UV coordinates to define the transparency of the mesh by using this nodegroup:






Blender Internal:


Enable Z transparency in Material settings &rarr; Transparency, and set alpha to 0:
  
To make the texture to affect the transparency of the material, enable Alpha in Texture settings &rarr; influence:



Another way to do this is by modifying the mesh only when rendered.

e.g with a boolean modifier: